We have also made some improvements to the CFR for situations where some environmental information cannot be known. We use the \(r^{\prime }\) , which adds to information gain, obtained in Equation (REF ) as one of the environmental information sources for CFR. The information gain is added to the terminal node of the game tree. Due to the recursive and iterative characteristics of CFR, the information gain can affect each node from the bottom to top. Different from traditional CFR, which continuously reduces the exploitability to improve the strategy, the addition of information gain is able to keep the reward \(r^{\prime }\)  to the direction of environmental exploration to improve the effect. The large cost of time and space is always a difficulty in the problem of extensive games with imperfect information. Inspired by pruning [1]}, judging its arrival probability first for each node in the game tree. When the node is at a extremely low arrival probability, it will be regarded as a relatively invalid node and not be traversed in this round. For all remaining nodes, the player \(i\)  makes use of the current strategy \(\sigma ^{t}_{i}\)  to calculate the cumulative regret \(R_{t}\)  and the counterfactual value (CFV) \(v^{\sigma ^{t}}_{i}(h)\)  [2]}. Through the regret matching (RM) [3]} of regret value for each node, the \(\sigma ^{t}_{i}\)  can be calculated. In the end, a game tree with \(v^{\sigma ^{t}}_{i}(h)\) , \(R_{t}\)  and \(\sigma ^{t}_{i}\)  for all valid nodes can be obtained. The significance of the average cumulative regret value \(\bar{R_{T}}\)  and the average strategy \(\bar{\sigma ^{T}}\)  is that there is a non-negligible relationship between them and NE. Despite unknown environmental information is used in our method, our goal is still to minimize \(R_{T}\)  and improve the player's reward so that the average strategy approaches an approximate NE.
